Reamer holders of this type have been used to eliminate any axial offset between a fixed reamer receiving bushing and a bore to be reamed in the operation of reamers on machine tools. The tool receiving bushing must be very easy to displace radially so that the reamer follows the axial offset even when subjected to high axial pushing forces and an accurate bore is reamed. For this purpose, German patent No. 1,256,039 proposes to provide the Oldham coupling disc with axial holes in which balls are inserted. The diameter of the balls is larger than the thickness of the coupling disc so that the balls roll between radial faces of the tool receiving bushing and the holder affixed to the machine tool. Therefore, the axial pushing forces for the reamer are transmitted by these balls which also make the radial displacement possible. Due to the presently prevailing high pushing speeds and the resultant high axial pressures used in machine tools of this type, the balls rapidly are pressed into the radial bearing faces. This makes the radial displacement of the tool receiving bushing more difficult, with the result that the reamer is eccentrically guided and the reamed bore does not have the required precision. This tendency towards sluggish mobility is further enhanced because the cooling water transports reamed chips into the range of the coupling. The chips are rolled by the balls, fixed and cause permanent deterioration of the quality of the bearing faces.